If tanθ + cotθ = 5, then tan2θ + cot2θ is?

Answer: Option A

$$\begin{array}{rl}& \text{Given,}\\ & \text{tan}\theta +\cot \theta =5\\ & \Rightarrow \text{tan}\theta +\cot \theta =5\\ & \Rightarrow {\left(\text{tan}\theta +\cot \theta \right)}^2=5^2\\ & \left(\text{Squaring both sides}\right)\\ & \Rightarrow \text{ta}{\text{n}}^2\theta +{\cot }^2\theta +2\text{tan}\theta \cot \theta =25\\ & \Rightarrow \text{ta}{\text{n}}^2\theta +\text{co}{\text{t}}^2\theta =\text{25}-\text{2}\\ & \left[\because \text{tan}\theta .\cot \theta =1\right]\\ & \Rightarrow \text{ta}{\text{n}}^2\theta +\text{co}{\text{t}}^2\theta =23\end{array}$$